A predator prey model with sparrssing effect is considered as follows:=x(ax-cx3-by);=y(-α+βx-γy)(*). The main result is as follows: (1) when A1<A1,A2<A2,A3>A3,there at leastn exists a limit cycle of the system(*); (2) when A22,A3>A3,there exists unique limit cycle of the system(*).